Problem: Ashley is 3 times as old as Emily. Sixteen years ago, Ashley was 7 times as old as Emily. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Ashley and Emily. Let Ashley's current age be $a$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $a = 3e$ Sixteen years ago, Ashley was $a - 16$ years old, and Emily was $e - 16$ years old. The information in the second sentence can be expressed in the following equation: $a - 16 = 7(e - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $a$ and substitute it into our second equation. Our first equation is: $a = 3e$ . Substituting this into our second equation, we get: $3e$ $-$ $16 = 7(e - 16)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $3 e - 16 = 7 e - 112$ Solving for $e$ , we get: $4 e = 96.$ $e = 24$.